Question

5.Industry statistics shows that the population standard deviation of the price of a gallon of gas is $0.03 A local gas station claims that their average price of a gallon gas is $1.23. You feel this claim is low. Taking a sample of the gas prices for 45 days, you find the sample average price is $1.24. Using a level of significance of .05, is the gas station’s claim low?

Answer 1

I Given a population ( price of a gallon I of gas ) with standard deviation, 0_80.03. we need to check whether the gas station's claim (average price of gallon gas) pes population means, fe is less than $1.23 : for that a saluple of size, n=45 is taken with sample means, X=$1.27 : we need to cheek at 2=0.05 level of significance. for that, the null and alternate hypothesis will be, Ho: M= 1-23 v/s Hi. M<1.23. which i ŭ a left-tailed test and since population standard deviation is known we use z test for population mean to check the claim

i critical z left taited ) value The rejection region for the test the te on 7 0:2 = 70.05 = -1.64 C-ve sign sime | Rejection region, R={2: 22-1647 1 Test statistic, z= P_ 1.23 - 1.24-1.23 In 0.03/rus = 2.236 Z= 2.236 7, Zc=-1-64, we can conclude that the null hepothesis is not rejected. That is there is not enough evidence to claim that the average price of gallon gas is less than $1.23.